Have you looked into Postural Orthostatic Tachycardia Syndrome? Something to consider given her heart rate increases (over 40 beats for children) so much from posture changes. It is a form of dysautonomia. There is a great website Dysautonomia international .org that has tons of information.
Agree with serana mostly, fits the bill for postural/vagal type of syndrome. Id be most suspicious for that.
Also fits the bill for other conduction system disorders involving accessory pathways, such as wolf parkinson white, which is easily ruled out via ekg, which im assuming shes had already.
In any case the condition doesnt sound like anything serious or dangerous. Biggest concern would be if she were to start passing out as a result of the episodes, in which case the worry is that shed take a fall and hurt her self as opposed to actual damange to the heart per se.